Physics

Masses of 6 kg and 2 kg are tied to the ends of a light string which passes over a light smooth pulley. The mass of 6 kg is held 1 m above the floor while the mass of 2 kg is resting on the floor. Find the upward displacement of the 2 kg mass when the system is released.
Assume g = 10m/s^2
When the system is released,
let acceleration = a, tension = T
6a = 6g - T
2a = T - 2g
Therefore,
8a = 4g
a = g/2 = 5 m/s^2
When 6kg mass reach ground, upward velocity of 2kg mass is given by
v^2 = 2a(1) = 10
v = 3.16m/s
2kg mass then under gravitational acceration g, it will further move upward by
0 = v^2 -2g(s)
s = 10/20 = 0.5m
Hence the 2kg mass will totally move upward by 1m + 0.5m = 1.5m